A Study on Interference of Surface Model Footings Resting on Sand

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Journal - The Institution of Engineers, Malaysia (Vol. 67, No. 1, March 2006) 15

A STUDY ON INTERFERENCE OF SURFACE MODEL

FOOTINGS RESTING ON SAND

Iqraz Nabi Khan1, K.C.Bohara2, M.L.Ohri3 and Alam Singh4

1Professor and Head, Department of Civil Engineering, Sri Balaji College of Engineering and Technology, Benad Road,

Jaipur-302013, Rajasthan, India.2

Assistant Engineer, Irrigation Department, Jodhpur, Rajasthan, India.3Former Professor, M.B.M. Engineering College, Jodhpur, Rajasthan, India.

4Former Professor and Head, M.B.M. Engineering College, Jodhpur, Rajasthan, India.

E-mail: [email protected]

1. INTRODUCTIONAll the structures, which exist on the earth, are ultimately

supported by the earth. The loads of a structure are transmitted

to the ground through its lowest structural element called the

foundation. In addition to the foundation material, the destiny

of a structure also depends on the properties of the patch of the

earth, rock or soil, on which the structure stands. So a

foundation engineer is concerned with the twin problems of

evaluating the ability of the earth to support the loads and

designing the proper transition members to transmit the

superstructure loads to the ground. The foundation design is

aimed at providing a means of transmitting the loads from a

structure to the underlying soil without causing any shearfailure or excessive settlement of the soil under the imposed

loads. Thus the choice of a suitable bearing capacity of soil

becomes the most important point to be considered in any

project. Bearing capacity, the supporting power of a soil or

rock, may be determined by analytical methods, conducting

field and laboratory tests and from the building codes. Soil

characteristics, position of water table, types of foundation and

their location are some of the factors which affect the bearing

capacity and the performance of a foundation.

The conventional theories on bearing capacity deal with

ideal situation. Inadequacies of these theories have been

experienced by many when met with situations, which deviate

from those assumed in these theories. When a locality is under-

developed and the foundation units are farther apart, the

adoption of conventional methods for computing the bearing

capacity is quite justified. But as the area goes on developing,

the proximity of the buildings to each other has a definite

influence on the bearing capacity and settlement characteristics

of footings. The interaction of pressure bulbs and failure

surfaces in closely placed footings change their bearing

capacity and settlement. This has provided the direction for

research on behaviour of interfering (adjacent) footings.

Model studies conducted on purely cohesionless soil by

Stuart [1] showed an increasing trend of bearing capacity with

decreasing spacing when pair of footings were brought closer

from large distance achieving a maximum at a spacing of about

1 to 1.5 times width of the footing. The failure surfaces were

also drawn and ultimate capacity for the pair was worked out.

The results of this theoretical investigation were not in close

agreement with the observed. Stuart [1] presented the results in

the form of non-dimensional charts. Stuart [1] was concerned

only with the interference between two footings. Mandel [2]

investigated a more general problem with structures on either

side of a footings. He developed the solution for an ideal soil

considering it as a weightless material. It is evident from his

curves that as the spacing between the footings decreases, the

bearing capacity increases. This is in general agreement to thework of Stuart [1]. Amir [3] obtained the tilt in case of hinged

footings and moments in the case of restrained footings from

the theoretical investigations on a pair of strip footings. Saran

and Aggarawal [4] conducted tests on sands and found that

bearing capacity of two interfering footings decreases rapidly

with the increase in spacing up to a spacing of 4.5 times width

of the footing beyond which it decreases slowly and attains

value of the bearing capacity of isolated footings. The extent of

failure surface decreases with the increase in spacing. Amir [5],

Kumar [6], Kumar and Saran [7], Kumar and Saran [8], Bohra

[9], Khan [10] and other investigators have also studied the

effect of interference between footings. Significant

improvement in bearing capacity computations have been made

through investigations on the effect of various factors including

interference of footings, which is not considered in the

conventional theories of bearing capacity. In practice, footings

may not be isolated due to the proximity of a nearby footing

leading to interference between them. In such cases effect of

interference should be taken into account. However, this fact is

usually not taken into consideration in design of foundations.

In brief it may be said that important changes in bearing

capacity and settlement characteristics occur when a footing is

placed in close proximity of a loaded footing. The centre to

centre spacing is the most significant parameter influencing the

ABSTRACT A model study has been conducted on the effect of interference of footings on bearing capacity and settlement of surface square,

circular and strip footings resting on sand. One footing was loaded to its safe bearing capacity and increments of load were

applied to an adjacent footing till complete failure of sand occurred. The efficiency of interfering footings have been compared

to that of the isolated footings having the same size from the considerations of bearing capacity and settlement characteristics.

The interference between footings was observed to cause an increase in bearing capacity and decrease in settlement with

reduction in spacing.

Keywords: Circular Footing and Strip Footing, Interference of Footings, Model Footings, Square Footing

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Journal - The Institution of Engineers, Malaysia (Vol. 67, No. 1, March 2006)

IQRAZ NABI KHAN, et al.

16

interference of footings. Other parameters that

affect the performance of adjacent footings are: type

of soil, density of soil, type of footing, roughness of

footing and depth of footing.

In this study one footing was loaded to its safe

bearing capacity and increments of load were

applied to an adjacent footing till complete failure

of sand occurred. The ultimate bearing capacity andsettlement characteristics of this adjacent footing

has been compared to that of the isolated footings

having the same size. Performance of the adjacent

footings has also been referred as performance of

group of footings.

2. DEVELOPMENT OF TESTPROGRAMME2.1 Soil Used

Dry sand was used for the study. Salient

properties of the sand are: 100% passing through 2

mm sieve, coefficient of uniformity cu = 1.5,

coefficient of curvature cc = 0.87, specific gravity G

= 2.66, proctor’s density = 16.57 kN/m3, minimum

density = 14.68 kN/m3, maximum density 17.2kN/m3, optimum moisture content = 11.63%,

density achieved for the study = 16.5 kN/m3, angle

of internal friction (dry) = 36˚, angle of internal

friction (submerged) = 33.5˚, permeability of sand =

0.453 x 10-3 mm/s and was classified as poorly

graded sand (SP), according to the classification

system of the Bureau of Indian Standards [11,12].

2.2 FootingsRough model footings of size 4 cm x 4 cm, 5 cm

x 5 cm, 7 cm x 7 cm, 15 cm x 6 cm and circular

footings of diameter 5 cm, 6 cm and 7 cm were

selected for the study. Model footings were moulded

from aluminium alloy. An emery cloth of extra-finegrade J298-EAwas pasted on the base of the footing

to make it rough. Arrangements were made for

normal transmission of the load.

2.3 TankThe size of tank was 100 cm x 50 cm in plan and 50 cm in

depth. The tank was made of angle iron and wooden planks

(Figure 1). The tank was designed to be used for circular

footings, square footings and strip footings. When the tests

were required to be conducted on strip footings, another tank

of size 70 cm x 16 cm x 40 cm was kept inside the bigger tank

(Figure 2) to facilitate the use of 15 cm x 6 cm size footings in

plane strain condition. Details of tank are given elsewhere such

as by Khan [10].

2.4 Loading SystemDead load system of loading was used. One frame was used

to load the footing, which represented existing footing, to safebearing capacity of footing. Another frame was used to apply

increments of load to adjacent footing till complete failure of

sand occurred.

2.5 Tests PerformedTests were performed on isolated footing and in group at

four S/D ratios; as shown in Table 1, where S is the spacing

between footings, B is the width of footings and D is the

diameter of the footings. Figure 1: Setup of apparatus

Figure 2: Experimental Setup (Loading Tank)





A STUDYON INTERFERENCE OF SURFACE MODELFOOTINGS RESTING ON SAND

17

2.6 Test ProcedureDry sand was compacted in layers of 15 cm thickness with

simultaneous working of two form vibrators fitted on a mild

steel plate for one minute, which gave a density of 16.5 kN/m3.

After compacting and levelling the sand, frames were fixed in

desired position and model footings were placed under the

proving ring suspended from the loading frames. A seating load

of 7 kN/m2 was applied and then released to ensure the contact

between the base of footing and surface of sand, which was in

accordance with the methods of Bureau of Indian Standards

[13]. Load was applied through steel ball and settlement of footing for each load increment was recorded using dial gauges.

Load was applied on the footings in increments till failure of

sand occurred. Each test was repeated for at least three times and

average load intensity-settlement curve was plotted for the tests.

3. TEST RESULTSLoad intensity was plotted against the corresponding

settlement of the footings and an average curve was obtained for

each set. The curves, in general, show a linear variation in the

initial portion and become non-linear thereafter. Figure 3 shows

average load intensity-settlement curve for isolated square

footings. Load intensity-settlement curve for group of square

footings placed at different S/B ratios are given in Figures 4, 5

and 6. Figure 7 shows average load intensity-settlement curvefor isolated strip footing and group of strip footings placed at

different S/B ratios. Figure 8 shows average load intensity-

settlement curve for isolated circular footings. Load intensity-

settlement curve for group of circular footings placed at different

S/D ratios are given in Figures 9, 10 and 11. These plots were

used for interpretation and deriving conclusions. Three ultimate

load criteria i.e. tangent-intersection method, log-log plot

method and collapse load criteria, have been used. All these

criteria require that loading tests should be carried out to large

displacements. The ultimate bearing capacity for square, strip

and circular footings obtained by the above methods have been

presented in Tables 2, 3 and 4 respectively, where S is thespacing between footings, B is the width of footings and D is the

diameter of footings.

The ultimate bearing capacity obtained using tangent

intersection method, which is quite common in use due to

convenience, was adopted for evaluating interference factors.

The failure surfaces formed on sand at the time of collapse of

the footing were extended to about 2 to 3 times the width

(diameter) of isolated footings. The footings failed by general

shear failure mode as witnessed by the sudden collapse of

Table 1: Tests performed on model footings

S. No. Size of Footing S/B or S/D Ratio

1 4 cm x 4 cm 1.75, 2.5, 3, 4

2 5 cm x 5 cm 1.4, 2, 3, 4

3 7 cm x 7 cm 1, 2, 3, 4

4 15 cm x 6 cm 1, 2, 3, 4

5 5 cm diameter 1.4, 2, 3, 46 6 cm diameter 1.16, 2, 3, 4

7 7cm diameter 1, 2, 3, 4

Figure 3: Load Intensity (x 10 kN/m 2 ) v/s Settlement (mm) for Isolated Square Footings

Figure 4: Load Intensity (x10 kN/m 2 ) versus Settlement (mm) for 4 cm x 4 cm Square Footings

Figure 5: Load Intensity (x10 kN/m 2 ) versus Settlement (mm) for 5 cm x 5 cm Square Footings






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footing into the soil at the time of failure. More amount of heave

was observed between the footings and less amount of heave

was observed towards non-interfering edges of footings.

4. DISCUSSIONS AND INTERPRETATIONOF RESULTS

The ultimate bearing capacity increases as the size of footing

increases. This fact has been supported by all investigators. The

increase in the ultimate bearing capacity with the corresponding

increase in the size of footing has been presented in Figures 12

and 13. It is also evident from Tables 2 and 4.

The footings failed by general shear failure mode as

witnessed by the sudden collapse of footing into the soil at the

time of failure. More amount of heave was observed between the

footings and less amount of heave was observed in non-

interfering edges of footings.

An examination of Figures 4, 5, 6, 7, 9, 10 and 11 indicates a

significant effect on bearing capacity and settlement characteristics

of footings when the centre to centre spacing is varied from B to4B, in the case of circular footing, D to 4D. Bearing capacity of

interfering (group) footing decreases rapidly with the increase in

spacing up to a spacing of 4B and becomes almost equal to the

bearing capacity of an isolated footing. The increase in the ultimate

bearing capacity may be due to: (a) existing footing acts as a

surcharge for the adjacent footing and (b) at wider spacing no

interference takes place and each footing acts as an individual

(isolated) footing [Figure 14(a)]. As spacing is reduced, a condition

shown in Figure 14(b) arises, where the passive zones just

Figure 6: Load Intensity (x10 kN/m 2 )versus Settlement (mm) for 7 cm x 7 cmSquare Footings

Figure 8: Load Intensity (x10 kN/m 2 ) versusSettlement (mm) for Isolated Circular Footings

Figure 7: Load Intensity (x10 kN/m 2 ) versusSettlement (mm) for 15 cm x 6 cm Strip

Footing

Figure 9: Load Intensity (x10 kN/m 2 ) versusSettlement (mm) for 5 cm Diameter Footings

Figure 10: Load Intensity (x10kN/m 2 ) versusSettlement (mm) for 6 cm Diameter Footings

Figure 11: Load Intensity (x10 kN/m 2 ) versus Settlement (mm) for7 cm Diameter Footings






19

penetrate, however

there is no apparent

change in bearing

capacity value. If

spacing is further

reduced, passive zones

between the footings

start curtailing oneanother which results

in changes in stress

value and increase in

ultimate bearing

capacity of the group of

footings [Figure 14(c)].

Figures 15(a) to

15(c) show Interference

Efficiency Factor

‘Fγ ’(qultg /qulti) versus

S/B (or S/D) ratio for square, strip and circular model footings

respectively. Figures 16(a) to 16(c) show the average curve

between Interference Efficiency Factor ‘Fγ ’(qultg /qulti) and S/B

(or S/D) ratio for square, strip and circular model footings

respectively. Where qultg is the ultimate bearing capacity of a

footing placed in close proximity of an already loaded footing

to its safe bearing capacity and qulti is the ultimate bearing

capacity of an isolated footing, S is the centre to centre spacingbetween the footings of width B or diameter D. The ratio

qultg /qulti may be called as Interference Efficiency Factor ‘Fg’ for

bearing capacity. In order to predict the increased bearing

capacity of a square, strip and circular footings placed in a

group, the Interference Efficiency Factor ‘Fγ ’ can be introduced

in the Terzaghi’s bearing capacity equation (surface footings)

as below:

qult = 0.5 γ B Nγ Fγ (strip footing)

qult = 0.4 γ B Nγ Fγ (square footing)

qult = 0.3 γ B Nγ Fγ (circular footing) Figure 12: Load Intensity (x10 kN/m 2 )versus Width of Square Footings (cm)

Table 2: Failure load tables for square footings table 2a: collapse load criterion

4 cm x 4 cm 5 cm x 5 cm 7 cm x 7 cm

S/B Ratio Collapse Load (kN/m2) S/B Ratio Collapse Load (kN/m2) S/B Ratio Collapse Load (kN/m2)

1.75 157 1.4 186 1.0 220

2.0 135 2.0 180 2.0 200

2.5 123 3.0 165 3.0 167

4 116 4.0 145 4.0 150

Isolated 110 Isolated 135 Isolated 146

Table 2b: Log-log criterion


S/B Ratio Ultimate Load (kN/m2) S/B Ratio Ultimate Load (kN/m2) S/B Ratio Ultimate Load (kN/m2)

1.75 130 1.4 151 1.0 190

2.0 107 2.0 140 2.0 155

2.5 98 3.0 130 3.0 150

4 92 4.0 109 4.0 133


Table 2c: Tangent intersection criterion


S/B Ratio Ultimate Load (kN/m2) S/B Ratio Ultimate Load (kN/m2) S/B Ratio Ultimate Load (kN/m2)

1.75 128 1.4 155 1.0 180

2.0 93 2.0 134 2.0 153

2.5 91 3.0 124 3.0 126

4 85 4.0 108 4.0 122


Table 3: Failure load table for 15cm x 6 footings

S/B Ratio Failure Load (kN/m2)

Collapse Load Criterion Log-log Criterion Tangent Intersection Criterion

1.0 310 215 208

2.0 296 210 196

3.0 272 180 168

4.0 223 150 150

Isolated 220 145 147






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Where,

qult = Ultimate bearing capacity of adjacent footing (kN/m2),γ = Density of soil (kN/m3),

B = Diameter (width) of footing (m),

Nγ = Terzaghi’s bearing capacity factor and

Fγ = Interference Efficiency Factor.

Figures 17(a), 17(b) and 17(c) show the plots between non-

dimensional settlement ρg / ρi and S/B ratio at 30 kN/m2 load

intensity for square, strip and circular model footings, whereρg / ρi is

the ratio of the settlement of the adjacent footing at a given load

intensity to an identical isolated footing at the same intensity of

pressure; it may be referred as interference efficiency factor forsettlement Fρ. Figures 18(a), 18(b), and 18(c) show an average curve

between non-dimensional settlement ρg’/ ρi ’ (Fr) and S/B ratio at 30

kN/m2 load intensity for square, strip and circular footings.

The settlement behaviour of footing resting on sand shows that

the closely spaced footings stiffen the soil response and reduces the

settlement at a given load intensity.

The relationship between ρg’/ ρi ’ and S/B ratio for 1.0 mm, 2.0

mm and 3.0 mm settlement for average value of square footings

have been presented in Figure 19, where qg’ is pressure intensity of

Table 4: Failure load table for circular footingsTable 4a: Collapse load criterion

5 cm diameter 6 cm diameter 7 cm diameter

S/D Ratio Collapse Load (kN/m2) S/D Ratio Collapse Load (kN/m2) S/D Ratio Collapse Load (kN/m2)

1.4 148.0 1.16 198.0 1.0 245.0

2.0 142.0 2.0 169.0 2.0 220.0

3.0 131.0 3.0 155.5 3.0 205.0

4.0 123.0 4.0 149.0 4.0 165.0

Isolated 121.0 Isolated 142.0 Isolated 155.0

Table 4b: Log-log criterion

5 cm diameter 6 cm diameter 7 cm diameter

S/D Ratio Collapse Load (kN/m2) S/D Ratio Collapse Load (kN/m2) S/D Ratio Collapse Load (kN/m2)

1.4 140.0 1.16 190.0 1.0 230.0

2.0 136.0 2.0 170.0 2.0 192.0

3.0 122.0 3.0 147.5 3.0 180.0

4.0 96.0 4.0 135.0 4.0 147.0


Table 4c: Tangent intersection criterion

5 cm diameter 6 cm diameter 7 cm diameterS/D Ratio Collapse Load (kN/m2) S/D Ratio Collapse Load (kN/m2) S/D Ratio Collapse Load (kN/m2)

1.4 124.0 1.16 149.0 1.0 164.5

2.0 116.0 2.0 127.0 2.0 139.0

3.0 100.0 3.0 118.0 3.0 130.0

4.0 97.0 4.0 109.0 4.0 118.0


Figure 13: Load intensity (x10 kN/m 2 ) versus diameter (cm) of footings

Figure 14: The development of the failure surfaces as two rough based foundations approach each other on the surface of a cohesionless soil

Figure 15(a): Interference efficiency factor ‘Fγ ’ versus S/B ratio(square footings)






21

Figure 15(b): Interference efficiency factor ‘Fγ ’ versus S/B ratio(strip footings)

Figure 15(c): interference efficiency factor ‘Fγ ’ versus S/D ratio(circular footings)

Figure 16(a): Average interference efficiency factor ‘Fγ ’ versusS/B ratio (square footings)

Figure 16(b): Average interference efficiency factor ‘Fγ ’ versusS/B ratio (strip footings)

Figure 16(c): Average interference efficiency factor ‘Fγ ’ versusS/D ratio (circular footings)

Figure 17(a): Fρ ( ρ g / ρi) versus S/B ratio at 30 kN/m 2 intensity for square footings

Figure 17(b): Fρ ( ρ g / ρi) versus S/B ratio at 30 kN/m 2 intensity for strip footings

Figure 17(c): Fρ ( ρ g / ρi) versus S/B ratio at 30 kN/m 2 intensity for circular footings






22

group of footings at constant settlement and qi’ is the pressure

intensity of isolated footing at same settlement. For constant value

of settlement, the pressure intensity ratio qg’/qi’ decreases as S/B

ratio increases. Similar trend was observed for strip and circular

model footings.

Figure 20 shows

settlement versus S/B

ratio at equal load

intensity for strip

footings. It is clear

from the figures that

for equal loading

intensity, settlement of footing decreases with

decrease in spacing

and for equal

settlement, the loading

intensity was found to

increase with a

decrease in spacing of

the footings. Similar

trend was observed for

square and circular

model footings.

5. CONCLUSION

1.Bearing capacity of model footings increases as the size of footing increases.

2.Bearing capacity of interfering footing is more than that of

isolated footing of the same size.

3.Bearing capacity of interfering footing increases as spacing

between them decreases.

4.For equal settlement, the loading intensity was found to

increase with decrease in spacing of the footings.

5.Settlement for a given load intensity decreases as the spacing

between the footings decreases.

6.In order to predict the increased bearing capacity of a square,

strip and circular footings placed in a group, the Interference

Efficiency Factor ‘Fg’ can be introduced in the Terzaghi’s

bearing capacity equation as under:

qult = 0.5 γ B Nγ Fγ (strip footing)

qult = 0.4 γ B Nγ Fγ (square footing)

qult = 0.3 γ B Nγ Fγ (circular footing)

Where, qult = Ultimate bearing capacity of adjacent footing

(kN/m3),

γ = Density of soil (kN/m3),

B = Diameter (width) of footing (m),

Nγ = Terzaghi’s bearing capacity factor and

Fγ = Interference Efficiency Factor.

REFERENCES

[1] J. G. Stuart, “Interference Between Foundations With

Special Reference to Surface Footings on Sand”,

Geotechnique, Vol. 12, No. 1, pp. 15-23, 1962.

[2] J. Mandel, “Interference Plastique de Foundations

Superficielles”, Proceedings of International Conference

on Soil Mechanics and Foundation Engineering,

Budapest, September 1963.

Figure 18(a): Average Fρ ( ρ g / ρi) versus S/B ratio at 30 kNm 2

intensity for square footings

Figure 18(c): Average Fρ ( ρ g / ρi) versus S/B ratio at 30 kNm 2

intensity for circular footings

Figure 19: qg/qi versus S/B Ratio for Average Value of Square Footings

Figure 18(b): Average Fρ ( ρ g / ρi) versus S/B ratio at 30 kNm 2

intensity for strip footings

Figure 20: Settlement versus S/B Ratio at Equal Load Intensity for Strip Footings






23

[3] J.M. Amir, “Interaction of Adjacent Footings”,

Proceedings of Third Asian Regional Conference on

Soil Mechanics and Foundation Engineering, 1967.

[4] S. Saran and V. C. Aggarawal, “Interference of Surface

Footings in Sands”, Indian Geotechnical Journal, 1974.

[5] A.A.A. Amir, “Interference Effect on the Behaviour of Footings”. Ph.D. Thesis, University of Roorkee,

Roorkee, India, 1992.

[6] A. Kumar, “Interaction of Footings Resting on

Reinforced Earth Slab”. Ph.D. Thesis University of

Roorkee, Roorkee, India, 1997.

[7] A. Kumar and S. Saran, “Closely Spaced Rectangular

Footings on Sand”. Journal of The Institution of

Engineers (India), Volume 84, pp 27-32, May 2003.

[8] A. Kumar and S. Saran, “Closely Spaced Footings on

Geo-grid-Reinforced Sand”. Journal of Geotechnical

and Geoenvironmental Engineering, ASCE, pp 660-664,

July 2003.

[9] K.C. Bohra, “Interference Between Circular Footings

Placed on Sand”, M.E. Dissertation, University of

Jodhpur, Jodhpur, Rajasthan, India, 1986.

[10] I. N. Khan, “Group Behaviour of Footings on Dune

Sand”, M.E. Dissertation, Department of Civil

Engineering, Faculty of Engineering, University of

Jodhpur, Jodhpur, Rajasthan, India 1986.

[11] IS:1498-1970, Indian Standard on Soil Classification

for General Engineering Purposes, Bureau of Indian

Standards, Delhi.

[12] IS:2720 (Part XIV-1968), Indian Standard Method of

Test for Soils, Bureau of Indian Standards, Delhi.

[13] IS:1888-1971, Indian Standard Method of Load Test on

Soils, Bureau of Indian Standards, Delhi.


Documents

A Study on Interference of Surface Model Footings Resting on Sand